scholarly journals A Nonconstant Shape Parameter-Dependent Competing Risks’ Model in Accelerate Life Test Based on Adaptive Type-II Progressive Hybrid Censoring

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Yan Wang ◽  
Yimin Shi ◽  
Min Wu
Keyword(s):  
Maximum Likelihood ◽  
Competing Risks ◽  
Accelerated Life Test ◽  
Type Ii ◽  
Life Test ◽  
Unknown Parameters ◽  
Competing Risks Model ◽  
Accelerate Life Test ◽  
Dependent Competing Risks ◽  
Maximum Likelihood Estimations

In this paper, the dependent competing risks’ model is considered in the constant-stress accelerated life test under the adaptive type-II progressive hybrid-censored scheme. The dependency between failure causes is modeled by Marshall–Olkin bivariate Gompertz distribution. The scale and shape parameters in the model both change with the stress levels, and the failure causes of some test units are unknown. Then, the maximum likelihood estimations and approximation confidence intervals of the unknown parameters are considered. And, the necessary and sufficient condition is established for the existence and uniqueness of the maximum likelihood estimations for unknown parameters. The Bayes approach is also employed to estimate the unknown parameters under suitable prior distributions. The Bayes estimations and highest posterior credible intervals of the unknown parameters are obtained. Finally, a simulation experiment has been performed to illustrate the methods proposed in this paper.

scholarly journals Bound lengths for Burr-XII distribution under step-stress PALT

2017 ◽  
Vol 5 (2) ◽  
pp. 135
Author(s):  
Gyan Prakash
Keyword(s):  
Simulated Data ◽  
Accelerated Life Test ◽  
Type Ii ◽  
Life Test ◽  
Unknown Parameters ◽  
Bayes Prediction ◽  
Accelerated Life ◽  
Progressive Type ◽  
Random Removal ◽  
Burr Type Xii

Some inferences based on Step-Stress Partially Accelerated Life Test (SS-PALT) are discussed in the present article. The Progressive Type-II censoring criterion with Random Removal scheme is used for determining the Approximate Confidence Lengths and One-Sample Bayes Prediction Bound Lengths for the unknown parameters of the Burr Type-XII distribution. Based on the simulated data, the analysis of the present discussion has been carried out.

Reliability Estimation for Hybrid System under Constant-stress Partially Accelerated Life Test with Progressively Hybrid Censoring

2020 ◽  
Vol 14 (1) ◽  
pp. 82-94
Author(s):  
Xiaolin Shi ◽  
Pu Lu ◽  
Yimin Shi
Keyword(s):  
Maximum Likelihood ◽  
Confidence Intervals ◽  
Reliability Index ◽  
Bootstrap Method ◽  
Accelerated Life Test ◽  
Life Test ◽  
Unknown Parameters ◽  
Bootstrap Confidence Intervals ◽  
Accelerated Life ◽  
Approximate Confidence Intervals

Background: Reliability analysis for the systems with masked data had been studied by many scholars. However, most researches focused on a system that is either series or parallel only, and the component in the system is mainly exponential or Weibull. In engineering practice, it is often seen that the structure of a system is a combination of series and parallel system, and other types of components are also used in the system. So it is important to study the reliability analysis of hybrid systems with modified Weibull components. Objective: For the hybrid system with masked data, the constant stress partial accelerated life test is performed under type-II progressive hybrid censoring. These data from life test are used to estimate unknown parameters and reliability index of system. The research results will not only provide theoretical basis and reference for system reliability assessment but also favor the patents on partial accelerated life test. Methods: Maximum likelihood estimates of unknown parameters are investigated with the numerical method. The approximate confidence intervals, and bootstrap confidence intervals for parameters are constructed by the asymptotic theory and the bootstrap method, respectively. Results: Maximum likelihood estimations of unknown parameters and reliability index of system are derived. The approximate confidence intervals and bootstrap confidence intervals for unknown parameters are proposed. The performance of estimation of unknown parameters and reliability index are evaluated numerically through Monte Carlo method. Conclusion: The performance on maximum likelihood estimation method is effective and satisfying. For the confidence intervals of parameters, bootstrap method outperforms the approximate method.

Constant-Stress Accelerated Life Test with Competing Risks under Progressive Type-II Hybrid Censoring

2013 ◽  
Vol 712-715 ◽  
pp. 2080-2083 ◽  
Author(s):  
Yi Min Shi ◽  
Li Jin ◽  
Chao Wei ◽  
Hong Bo Yue
Keyword(s):  
Competing Risks ◽  
Failure Modes ◽  
Constant Stress ◽  
Accelerated Life Test ◽  
Type Ii ◽  
Life Test ◽  
Hybrid Censoring ◽  
Accelerated Life ◽  
Progressive Type ◽  
Mean Lifetime

In this paper, we consider a constant-stress accelerated life test with competing risks for failure from exponential distribution under progressive type-II hybrid censoring. We derive the maximum likelihood estimator and Bayes estimator of the parameter and prove their equivalence under certain circumstances. Further study of the estimators indicates that missing of failure modes would result in overestimation of the mean lifetime. Finally, a Monte-Carlo simulation is performed to demonstrate the accuracy and effectiveness of the estimators.

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